Equalizing network

ABSTRACT

An equalizing network for correcting delay and amplitude distortions has four bridge arms, including a first arm and a second arm constituted by different winding sections of an auto transformer. The first arm, connected across a source of input signal and a third arm in series therewith lie on one side of an output diagonal while the second arm lies on the other side of that diagonal in series with a fourth arm. The second arm is subdivided into two subsections respectively provided with n Eta and un(1 + Eta ) n) turns where n is the number of turns of the first section and u is a turn ratio related to a desired degree of attenuation to be introduced. The third and fourth arms include respective resistors R1 and R2 with magnitudes in the R2/R1 Eta ganged for concurrent adjustment to vary the phase shift, a tunable resonant circuit being included in one of these latter arms in the form of either a series-resonant circuit in line with R2 or a parallel-resonant circuit in shunt with R1.

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ATTORNEY United States Patent 1,681,532 8/1228 Gardner inventor Karl Heinz Feistel Eningen, Germany Appl. No. 819,894 Filed Apr. 28, 1969 Patented Mar. 2, 1971 Assignee Wandel u. Goltermann Rundfunk-und Messgeratewerk Fernmelde-Anlagen, Postfach, Reutlingen, Germany Priority Apr. 27, 1968 Germany P 17 62 201.4

EQUALIZING NETWORK 10 Claims, 16 Drawing Figs.

U.S. Cl 333/28, 333/70, 333/75 Int. Cl .r H03h 5/08, l-l03h 7/10, H03h 9/00 Field of Search 333/28, 70, 74,18, 75; 324/57 References Cited UNlTED STATES PATENTS 1,740,491 12/1929 Affel Primary Examiner- Herman Karl Saalbach Assistant Examiner-Marvin Nussbaum Attorney-Karl F. Ross tions of an auto transformer. The first arm, connected across a source of input signal and a third arm in series therewith lie on one side of an output diagonal while the second arm lies on the other side of that diagonal in series with a fourth arm. The second arm is subdivided into two subsections respectively provided with m and un(1 +17) turns where n is the number of turns of the first section and u is a turn-ratio related to a desired degree of attenuation to be introduced. The third and fourth arms include respective resistors R and R with magnitudes in the R lR 1; ganged for concurrent adjustment to vary the phase shift, a tunable resonant circuit being included in one of these latter arms in the form of either a seriesresonant circuit in line with R or a parallel-resonant circuit in shunt with R PATENIED I IAR 2197! 3 56 101 SHEEI 2 [IF 3 FIG.7

attenuation L n R 05 TI 2 v 1 m mg E n Lw R A K ATTORNEY EQUALIZING NETWORK My present invention relates to an equalizing network designed to correct delay and amplitude distortions in a signaling system serving for the transmission of a broad frequency band.

Such equalizers are used, e.g. in telecommunication channels, to compensate for the differences in attenuation and phase shifts of the various signal frequencies; for this purpose it is customary to employ a plurality of such equalizersconnected in cascade, each equalizer being assigned to a fraction of the overall frequency range. Generally, all pass networks such as lattice sections or bridge circuits are employed to that end. With an adjustable impedance included in a reactive arm of an otherwise resistive bridge circuit, the attenuation can be controlled by adjustment of the resistance ratio of two bridge arms whereas the phase angle at a selected midfrequency may be altered by varying the reactance and a resistance. Thus, a

, conventional equalizer of this type includes a parallel-resonant circuit in shunt with the resistance of one arm or a seriesresonant circuit in line therewith; with one of the reactances of the tuned circuit adjustable to establish a desired resonance frequency, two resistances must be separately adjusted to provide a selected phase shift and damping function. Since the setting of one of the attenuation controlling resistors depends on the chosen angle function, delay compensation and amplitude compensation cannot be carried out independently.

It is, therefore, the general object of my present invention to provide an improved equalizer of the character referred to in which these parameters may be adjusted substantially independently of each other.

A related object is to provide an equalizing network whose variable impedances can be adjusted in discrete and predeter mined increments for reproducibly establishing a selected state of attenuation and phase shift.

These objects are realized pursuant to my present invention, by the provision of a bridge circuit with a first arm and a second arm represented by inductively coupled windings, a first winding in the first arm having a fixed number of turns n whereas the winding or windings in the second arm have an effective number of turns equal to n['r u(l 1 where n is a constant (which for convenience may be equal to unity) and u is a variable related to a desired damping factor which, for a selected midfrequencyf is given (in decibels) by FA K? The several windings of these two arms advantageously form respective parts of an autotransformer. The combined windings have an alternating current signal developed thereacross by an input circuit which, owing to the autotransformer effect, needs to be connected only across one of these two windings, preferably the first one. With the third and fourth arms including respective resistances whose magnitudes are related to each other in the same ratio 1:1 as the turns of the first winding and of a fixed section of the second winding, a variable section of the latter winding establishes the desired numerical value u. The midfrequency f is the resonance frequency of a tuned circuit included in the third or the fourth bridge arm. The output signal is developed across a pair of terminals respectively tied to the junction of the first and second bridge arms and to the junction of the third and fourth bridge arms, the first of these terminals being common to input and output circuits in the preferred arrangement in which the input signal is applied only to the first winding. The resistances of the third and fourth arms are ganged for concurrent adjustment, without change in their relative magnitudes, to vary the peak of the delay curve occurring at resonance; this adjustment is independent of the peak attenuation a, which, upon a reversal of the winding connections in the second arm, may also assume negative values. The variable turn ratio u will be considered positive when the two winding sections of the second bridge arm are in series-aiding relationship.

The above and other features of my invention will become more fully apparent from the following detailed description of certain embodiments, reference being made to the accompanying drawing in which:

FIG. 1 is a block diagram ofa signal-transmission system incorporating a plurality of tandem-connected equalizers according to the invention;

FIG. 2 is a circuit diagram of a conventional equalizer also adapted to be used in the system of FIG. 1',

FIGS. 3 and 4 are circuit diagrams similar to FIG. 2, showing two representative embodiments of an equalizer according to my invention;

FIG. 5 shows a modification ofthe embodiment of FIG. 3;

FIG. 6 is a circuit diagram similar to FIG. 3 but using different designations for explanatory purposes;

FIG. 7 is a plot of a complex variable characterizing the transmission properties of the equalizer of FIG. 6', and

FIGS. 8, 8a, 8b, 8c, 9, 9a, 9b, 10 and 11 represent graphs of different parameters of the same equalizer plotted over a range of operating frequencies.

In FIG. I I have shown a signal transmission system comprising a transmitter 3 and a receiver 5 interconnected by a channel such as, for example, a coaxiai cable. The distributed impedances of this channel, causing relative phase shifts and amplitude distortions, have been symbolized diagrammatically at 4. Three equalizing networks 2,2 and 2", representative of any number of such networks connected in tandem, are designed to rectify these distortions in different ranges of the transmitted frequency band. Amplifiers 1, l, l" and 1", serving as impedance transformers, precede and follow each of the equalizing networks. Thus, amplifiers l, l, I" may serve as voltage sources for the immediately succeeding equalizers which work into high input impedances of amplifiers I, 1", 1" so as to have their outputs virtually open circuited to develop corrected load voltages. It is, however, also possible to energize the equalizers with driving current rather than driving voltage and to let them work into low-impedance amplifier inputs, constituting virtual short circuits therefor, for the generation of corrected load currents.

A prior art network 20, adapted to be used for any one of the equalizers of FIG. 1, has been shown in FIG. 2. It comprises, essentially, a bridge circuit or lattice section with a first resistance arm 21, a second resistance arm 22, a third arm with a variable resistor 23 shunted by a parallel-resonant network consisting of a fixed capacitor 25 and an adjustable inductance 24, and a fourth arm constituted by a variable resistor 26. If an alternating current signal of frequency f,, is impressed upon the input diagonal of the network represented by terminals I and II, the relative amplitude of the input signal developed across the diagonal represented by terminals III and IV depends exclusively on the relative magnitudes of resistances 21, 22, 23 and 26. Thus, the bridge would be in balance if the ratio of resistance 21 and 22 were the same as that of resistances 23 and 26, this situation corresponding to infinite attenuation with zero output. In order to select a desired damping factor, these ratios must therefore be mutually different. On the other hand, after adjustment of coil 24 to tune the resonant network to a selected midfrequency f,,, resistor 23 must also be adjusted to provide the proper phase shift at that frequency. This, in turn, necessitates a resetting of resistor 26 whenever the phase shift needs changing while the attenuation is to remain constant.

In FIG. 3 I have shown an improved equalizing network 30 embodying my invention. This network also has four bridge arms, i.e. a first arm in the form of a winding 31 of an autotransformer 34, a second arm comprising two further windings 32, 33 of the same autotransformer 34, a third arm constituted by an adjustable resistor 36, and a fourth arm including another adjustable resistor 37 in series with a fixed inductance 38 and a variable capacitor 39. A switch 310 enables relative inversion of the polarities of windings 32 and 33, the latter being provided with a set of taps selectively engageable by a slider 35 to vary the effective number of turns of this winding. Input terminals 1 and II are tied to opposite extremities of winding 31, terminal II being also connected via a conductor 311 (which may be grounded) to output terminal [V which, like the associated terminal III, is connected to the same junction as in FIG. 2.

FIG. 4 shows an analogous network according to my inven tion wherein elements 4l47, 410 and 411 correspond to elements 31-37, 310, 311 of FIG. 3. It will be noted that in this case, as in the conventional equalizer of FIG. 2 the series-resonant circuit 38, 39 of FIG. 3 has been replaced by a parallelresonant circuit shunted across the resistor 46, this resonant circuit consisting of a fixed capacitor 48 and a variable inductance 49 similar to impedances 25 and 24 of FIG. 2.

The resistors 36 and 37 (FIG. 3) or 46, 47 (FIG. 4) in the third and fourth bridge arms are ganged for concurrent adjustment without change of their relative magnitudes. Instead of being continuously variable, their resistances may be adjustable in discrete correlated increments for greater exactitude in the selection of a desired phase shift as more fully described hereinafter. A similar incremental selection of the turn ratio between the combined first and second autotransformer windings 31, 32 or 41, 42, on the one hand, and the third winding 33 or 43, on the other hand, is provided by the contactor 35 or 45. This turn ratio, designated u, can be selectively varied between values greater than, equal to or smaller than unity.

A more elaborate arrangement for adjusting the turn ratio 14 is shown in FIG. 5 with reference to an equalizer 50 generally similar to that of FIG. 3, with corresponding elements analogously designated except for a substitution of the first digit 3 by 5." In this network the third winding 53 of autotransformer 54, here shown interposed between the other two windings 51 and 52, is coupled via two cascaded autotransformer stages 512, 513 and two tandem-connected reversing switches 510, 514 in series with windings 51 and 52, its own turn ratio being multiplied by the adjustable turn ratios of stages 512 and 513. FIG. 5 further shows the adjustable resistors 56 and 57 shunted by other resistors 56a, 57a also interconnected for concurrent adjustment; the resistors of each pair such as 56 and 56a may be decadically related so that the combined conductance of the pair may be varied in unit steps by the smaller resistor 560 (or 57a) and in l-unit steps by the larger resistor 56 (or 57). An analogous decadic arrangement in the network of FIG. 4 would require the insertion of ancillary resistors in series with resistors 46 and 47, respectively, the resistors of each pair being then calibrated in unit and l0-unit resistance steps rather than conductance steps as in FIG. 5.

While the networks of FIGS. 3 and 4 are largely equivalent, the choice of a series-resonant circuit (FIG. 3) will generally be indicated where the copper losses of the coil 38 predominate (since these losses may be partly compensated by a corrective dimensioning of series resistance 37) whereas a parallel-resonant circuit (FIG. 4) will be preferred if the inductance 49 has a large shunt conductance. In FIG. I have symbolically indicated the copper losses of coil 58 by a resistor 515 in the fourth bridge arm, a compensating resistor 515 being included in the third arm in series with resistor combination 56, 560. An analogous arrangement has been shown in FIG. 4 where the shunt conductance of coil 49 has been represented by a resistance 415' in the third arm, a compensating resistor 415 having been connected across resistor 47 in the fourth arm.

In the following discussion I shall, for simplicity, consider only an equalizer of the series-resonant type as shown in FIGS. 3, 5 and 6, it being understood that analogous relationships obtain in a parallel-type equalizer as shown in FIG. 4. In any event, the resistors associated with the tuned circuits are to be so connected that their calibrated resistances or conductances effectively control the damping of the network at resonance.

In FIG. 6 I have marked the three windings ofthe autotransformer by their effective number of turns, i.e. a basic number n in the case of the first winding, a related number rm in the case ofthe second winding and a number un(l n) in the case of the third winding. The magnitudes of the resistors in the third and fourth arms, here designated R, R and R 'r R, are related in the same ratio as the turns of the first two windings. The virtual resistance in the fourth arm, representing the copper losses of coil L in series with condenser C, has been designated R,.', its compensating resistance in the third arm being shown at R,.. The switchover means for reversing the relative polarity of the adjustable third winding with reference to the fixed second winding has been designated S. At E, and E I have indicated the input and output voltages developed across terminal pairs 1, II' and III, IV.

The transmission function of the network shown in FIG. 6 can be calculated as follows:

Let V, be the voltage developed, in response to input voltage E,, across the three serially connected autotransformer windings in the first and second bridge arms, and let V be the voltage developed across the resistance R, of the third arm. Neglecting the resistances R, and R,.', we can then write 1 1( l)( and V V,R ;1 (1+ )+Z sncs. ii: F

R u+ E2 1 7 R0 +2 where Z=jw (L I we (4) with m 2117). I

The ratio K of the input and output voltages of the network is then found to be 1 E1 U 1) +1 -5 E 1 +n) +.7 (5) which yields w +jw(1 +11) L LC For convenience of calibration, e.g. to measure phase delays reading in whole numbers of milliseconds or microseconds rather than in fractional numbers of seconds, we shall introduce a freely selectable reference frequency m/w,=Q.

(I) J an- (7) whence v I v 2 R 1 K: 0 (1+77) w L w LC 2 l a @,L wLC 8 Since the numerator and the denominator of equation (8) are second-order polynomials in 0, we can rewrite this equation as K: 24) (0 0N) (0-0?) where t9 and Q, are the zeros or nodes of the function K whereas 6 and 0,. are the poles thereof.

Solving separately for 0 and (J we obtain (1+ 1)R 1 1 R N= i ZZZ- E R0,, i m

and

(l+n)uR j L 1+ MR enc The corresponding phasors have been plotted in FIG. 7 which indicates that the real terms Rd,- (or R0,.) are the same for both conjugate values t9, (01' 0 0 and that their imaginary terms 2 I 0 (or M are of opposite signs.

From the foregoing equations we can derive the following 5 expressions for the absolute values and real terms of the angle parameters 0 and 9 whereas the attenuation factor or, for the resonance frequency )2, can be derived from the previously given relationship between this factor and the turn ratio u as It will thus be seen that the resonance parameter (I, can be varied simply by adjustment of the tuning capacitance C (or the tuning inductance in the parallel-resonant network of FIG. 4) which does not intervene in the formula for the time constant T It will also be noted that the turn ratio u, which alone controls the damping factor a does not appear in the equations for the other two parameters. Thus, independent selection of these three parameters is possible with the aid of simple controls.

a (db)=20 log =20 log If the reversing switch S of FIG. 6 is operated, the ratio u as sumes negative values; this, however, affects only the poles 0 and 0;. which thereupon acquire negative instead of positive real terms so as to become the phasors 0 and 0,, illustrated in dot-dash lines in FIG. 7.

The frequency-controlling reactance C or L may likewise be variable in discrete increments. For a given equalizer in the chain of FIG. 1, this reactance may also be fixed or only limitedly adjustable to prevent coincidence of the midfrequeneies of different equalizer stages.

In the presence of compensating resistor R equation (16) is modified to read where v e ML 18) The real term of 0,, then becomes it?) (i R0N 2 -lso that the smallest realizable value of this term is given by l xReN1m..=%E

With the capacitance C of the series-resonant circuit or the inductance L of the parallel-resonant circuit going toward infinity, the imaginary terms in the diagram of FIG. 7 disappear; these types of equalizers may be used for some of the stages of the chain of FIG. 1.

FIG. 8 shows the variation of the attenuation a with different values of Q. The variable a reaches its maximum value a, at the resonance frequency represented by O. 0,.

FIG. 8a shows a family of curves representing the function a for different values of 0 the peak attenuation a, and delay time T, being held constant.

FIG. 8b shows the variations of a with different values of T,,, with a, and (I, both constant.

FIG. shows how the magnitude of a varies throughout the operative frequency range with selection of different peak values 01 of either sign, as established by positive and negative turn ratios u, with n and T held constant.

FIG. 9 shows the variation of the delay time T throughout the frequency range, the maximum T being reached with Q Q Curve T is a composite of two curves T and T which, for the sake of clarity, have been extended to the hypothetical region of negative frequencies. FIGS. 9a and 9b show the behavior of Twith different values of Q, a and 0,, being con stant.

FIG. 10 shows the function T with positive values of u (switch S of FIG. 6 in its normal position), together with the function T applying to negative values of :4 (switch S reversed), both plotted against frequency f. The attenuation a, which is independent of the sign of u as per equation 17, is the same for both cases.

FIG. 11 shows the overall functions T and T for a chain of equalizers according to the invention, connected in tandem as illustrated in FIG. 1.

From FIGS. 10 and 11 it will be noted that the delay time T' varies only slightly throughout the fgequency ba nd, owing to the relative closeness of phasors O O and 0 6 in FIG. 7;

5 thus, the use of my improved equalizer with its switch S reversed may be desirable in situations requiring only the amplitude distortions to be corrected. With a chain of equalizers as shown in FIG. 1 tuned to progressively higher (or lower) resonance frequencies, it may be advantageous to employ such a series-opposed connection of the second and third autotransformer windings at the stages assigned to the lowest and the highest range of the transmitted frequency band.

In adjusting the equalizing network according to my invention to a desired set of parameters, I may first select the values of T, and 0,, by adjusting the ganged resistors 36, 37 (FIG. 3) or 46, 47 (FIG. 4) and the variable reactance 39 (FIG. 3) or 49 (FIG. 4) in the aforedescribed manner, whereupon a is chosen with the aid of, say, the slider 35 or 45 controlling the 0 turn ratio of the autotransformer. Since 0 is a function of u,

substantial changes in a, may affect the shape of curve Tto an undesirable extent. This may be remedied by a readjustment of the delay selector to reduce the magnitude of T of the affected equalizer stage by a factor p equal to /m,

thereby replacing R0,, in equation (16) by the geometric 1 mean of the absolute values of R6,, and RE For u= i approximately corresponding to an attenuation of 10 db, p z 0.6.

I claim:

1. An equalizing network comprising a bridge circuit with a first, a second, a third and a fourth arm; said first and second arms including inductively coupled first and second winding means, respectively, connectable to a source of current for the development of an alternating-current signal thereacross, said second arm further including control means for varying the effective turn ratio 1 z [n u(l 1 of said first and second winding means where 1 is a constant and u is a variable determining the damping factor of The network, said third and fourth arms respectively including first and second resistance means ganged for concurrent adjustment of their magnitudes 5 with an invariable ratio 1 "r; to vary the angle function of the network, one of the two last-mentioned arms also including variable reactance means; and a pair of output terminals at the junction of said first and second arms and at the junction of said third and fourth arms, respectively.

2. A network as defined in claim 1 wherein said second and winding means is divided into a fixed section of m; turns and a variable section of un (l 1;) turns where n is the number of turns of said first winding means.

3. A network as defined in claim 2 wherein said variable section includes an added winding and adjustable transformer means coupling said fixed section to said added winding.

4. A network as defined in claim 2 wherein said second arm is provided with switchover means for reversing the connection between said fixed and variable sections.

5. A network as defined in claim 2 wherein said bridge circuit is provided with an input circuit connected across said first arm only, said first winding means and said fixed and variable sections being respective parts of an autotransformer.

6. A network as defined in claim 2 wherein the other of the two last-mentioned arms includes a supplemental resistance for compensating the copper losses of said variable section.

7. A network as defined in claim 1 wherein said reactance means comprises a capacitance and an inductance constituting a tuned circuit, said tuned circuit being connected to the associated resistance means for effective dampin'g thereby at a resonant frequency.

8. A network as defined in claim 7 wherein said tuned circuit is a parallel-resonant circuit in shunt with said first resistance means.

9. A network as defined in claim 7 wherein the said tuned circuit is a series-resonant circuit in series with said second resistance means.

10. A signal-transmission system including a plurality of equalizing networks as defined in claim 1, connected in cascade, and impedance transforming means inserted between said equalizing networks. 

1. An equalizing network comprising a bridge circuit with a first, a second, a third and a fourth arm; said first and second arms including inductively coupled first and second winding means, respectively, connectable to a source of current for the development of an alternating-current signal thereacross, said second arm further including control means for varying the effective turn ratio 1 : ( Eta + u(1 + Eta )) of said first and second winding means where Eta is a constant and u is a variable determining the damping factor of The network, said third and fourth arms respectively including first and second resistance means ganged for concurrent adjustment of their magnitudes with an invariable ratio 1 : Eta to vary the angle function of the network, one of the two last-mentioned arms also including variable reactance means; and a pair of output terminals at the junction of said first and second arms and at the junction of said third and fourth arms, respectively.
 2. A network as defined in claim 1 wherein said second and winding means is divided into a fixed section of n eta turns and a variable section of un (1 + eta ) turns where n is the number of turns of said first winding means.
 3. A network as defined in claim 2 wherein said variable section includes an added winding and adjustable transformer means coupling said fixed section to said added winding.
 4. A network as defined in claim 2 wherein said second arm is provided with switchover means for reversing the connection between said fixed and variable sections.
 5. A network as defined in claim 2 wherein said bridge circuit is provided with an input circuit connected across said first arm only, said first winding means and said fixed and variable sections being respective parts of an autotransformer.
 6. A network as defined in claim 2 wherein the other of the two last-mentioned arms includes a supplemental resistance for compensating the copper losses of said variable section.
 7. A network as defined in claim 1 wherein said reactance means comprises a capacitance and an inductance constituting a tuned circuit, said tuned circuit being connected to the associated resistance means for effective damping thereby at a resonant frequency.
 8. A network as defined in claim 7 wherein said tuned circuit is a parallel-resonant circuit in shunt with said first resistance means.
 9. A network as defined in claim 7 wherein the said tuned circuit is a series-resonant circuit in series with said second resistance means.
 10. A signal-transmission system including a plurality of equalizing networks as defined in claim 1, connected in cascade, and impedance transforming means inserted between said equalizing networks. 